A new optimal eighth-order family of iterative methods for the solution of nonlinear equations

In this paper a new optimal family of methods for solving nonlinear equations is presented. It is proved by analysis of convergence that each member of the family, which requires three evaluations of the function and one evaluation of its first derivative per iteration, is of optimal order eight. Numerical comparisons are made with several other existing eighth-order methods by using the basins of attraction and through numerical computations to demonstrate the efficiency and the performance of the presented methods.